articles/ceaice/ceaice_intro.tex

\section{Introduction}
\label{sec:intro}

In recent years, ocean state estimation has matured to the extent that
estimates of the time-evolving ocean circulation, constrained by a multitude
of in-situ and remotely sensed global observations, are now routinely
available and being applied to myriad scientific problems \citep[and
references therein]{wun07}.  As formulated by the consortium for Estimating
the Circulation and Climate of the Ocean (ECCO), least-squares methods, i.e.,
filter/smoother \citep{fuk02}, Green's functions \citep{men05}, and adjoint
\citep{sta02a}, are used to fit the Massachusetts Institute of Technology
general circulation model
\citep[MITgcm;][]{marshall97:_finit_volum_incom_navier_stokes} to the
available data.  Much has been achieved but the existing ECCO estimates lack
interactive sea ice.  This limits the ability to utilize satellite data
constraints over sea-ice covered regions.  This also limits the usefulness of
the derived ocean state estimates for describing and studying polar-subpolar
interactions.  This paper is a first step towards adding sea-ice capability to
the ECCO estimates.  That is, we describe a dynamic and thermodynamic sea ice
model that has been coupled to the MITgcm and that has been modified to permit
efficient and accurate forward integration and automatic differentiation.

Although the ECCO2 optimization problem can be expressed succinctly in
algebra, its numerical implementation for planetary scale problems is
enormously demanding.  First, multiple forward integrations are required to
derive approximate filter/smoothers and to compute model Green's functions.
Second, the derivation of the adjoint model, even with the availability of
automatic differentiation tools, is a challenging technical task, which
requires reformulation of some of the model physics to insure
differentiability and the addition of numerous adjoint compiler directives to
improve efficiency \citep{marotzke99}.  The MITgcm adjoint typically requires
5--10 times more computations and 10--100 times more storage than the forward
model.  Third, every evaluation of the cost function entails a full forward
integration of the assimilation model and multiple forwards (and adjoint for
the adjoint method) iterations are required to achieve satisfactorily
converged solutions.  Finally, evaluating the cost function also requires
estimating the error statistics associated with unresolved physics in the
model and with incompatibilities between observed quantities and numerical
model variables.  These statistics are obtained from simulations at even
higher resolutions than the assimilation model.  For all the above reasons, it
was decided early on that the MITgcm sea ice model would be tightly coupled
with the ocean component as opposed to loosely coupled via a flux coupler.


Traditionally, probably for historical reasons and the ease of
treating the Coriolis term, most standard sea-ice models are
discretized on Arakawa-B-grids \citep[e.g.,][]{hibler79, harder99,
  kreyscher00, zhang98, hunke97}, although there are sea ice models
diretized on a C-grid \citep[e.g.,][]{ip91, tremblay97,
  lemieux09}. %
\ml{[there is also MI-IM, but I only found this as a reference:
  \url{http://retro.met.no/english/r_and_d_activities/method/num_mod/MI-IM-Documentation.pdf}]}
From the perspective of coupling a sea ice-model to a C-grid ocean
model, the exchange of fluxes of heat and fresh-water pose no
difficulty for a B-grid sea-ice model \citep[e.g.,][]{timmermann02a}.
However, surface stress is defined at velocities points and thus needs
to be interpolated between a B-grid sea-ice model and a C-grid ocean
model. Smoothing implicitly associated with this interpolation may
mask grid scale noise and may contribute to stabilizing the solution.
On the other hand, by smoothing the stress signals are damped which
could lead to reduced variability of the system. By choosing a C-grid
for the sea-ice model, we circumvent this difficulty altogether and
render the stress coupling as consistent as the buoyancy coupling.

A further advantage of the C-grid formulation is apparent in narrow
straits. In the limit of only one grid cell between coasts there is no
flux allowed for a B-grid (with no-slip lateral boundary counditions),
and models have used topographies with artificially widened straits to
avoid this problem \citep{holloway07}. The C-grid formulation on the
other hand allows a flux of sea-ice through narrow passages if
free-slip along the boundaries is allowed. We demonstrate this effect
in the Candian Arctic Archipelago (CAA).

Talk about problems that make the sea-ice-ocean code very sensitive and
changes in the code that reduce these sensitivities.

This paper describes the MITgcm sea ice model; it presents example
Arctic and Antarctic results from a realistic, eddy-permitting, global
ocean and sea-ice configuration; it compares B-grid and C-grid dynamic
solvers and investigates further aspects of sea ice modeling in a
regional Arctic configuration; and it presents example results from
coupled ocean and sea-ice adjoint-model integrations.

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1	\section{Introduction}
2	\label{sec:intro}
3
4	In recent years, ocean state estimation has matured to the extent that
5	estimates of the time-evolving ocean circulation, constrained by a multitude
6	of in-situ and remotely sensed global observations, are now routinely
7	available and being applied to myriad scientific problems \citep[and
8	references therein]{wun07}. As formulated by the consortium for Estimating
9	the Circulation and Climate of the Ocean (ECCO), least-squares methods, i.e.,
10	filter/smoother \citep{fuk02}, Green's functions \citep{men05}, and adjoint
11	\citep{sta02a}, are used to fit the Massachusetts Institute of Technology
12	general circulation model
13	\citep[MITgcm;][]{marshall97:_finit_volum_incom_navier_stokes} to the
14	available data. Much has been achieved but the existing ECCO estimates lack
15	interactive sea ice. This limits the ability to utilize satellite data
16	constraints over sea-ice covered regions. This also limits the usefulness of
17	the derived ocean state estimates for describing and studying polar-subpolar
18	interactions. This paper is a first step towards adding sea-ice capability to
19	the ECCO estimates. That is, we describe a dynamic and thermodynamic sea ice
20	model that has been coupled to the MITgcm and that has been modified to permit
21	efficient and accurate forward integration and automatic differentiation.
22
23	Although the ECCO2 optimization problem can be expressed succinctly in
24	algebra, its numerical implementation for planetary scale problems is
25	enormously demanding. First, multiple forward integrations are required to
26	derive approximate filter/smoothers and to compute model Green's functions.
27	Second, the derivation of the adjoint model, even with the availability of
28	automatic differentiation tools, is a challenging technical task, which
29	requires reformulation of some of the model physics to insure
30	differentiability and the addition of numerous adjoint compiler directives to
31	improve efficiency \citep{marotzke99}. The MITgcm adjoint typically requires
32	5--10 times more computations and 10--100 times more storage than the forward
33	model. Third, every evaluation of the cost function entails a full forward
34	integration of the assimilation model and multiple forwards (and adjoint for
35	the adjoint method) iterations are required to achieve satisfactorily
36	converged solutions. Finally, evaluating the cost function also requires
37	estimating the error statistics associated with unresolved physics in the
38	model and with incompatibilities between observed quantities and numerical
39	model variables. These statistics are obtained from simulations at even
40	higher resolutions than the assimilation model. For all the above reasons, it
41	was decided early on that the MITgcm sea ice model would be tightly coupled
42	with the ocean component as opposed to loosely coupled via a flux coupler.
43
44
45
46	Traditionally, probably for historical reasons and the ease of
47	treating the Coriolis term, most standard sea-ice models are
48	discretized on Arakawa-B-grids \citep[e.g.,][]{hibler79, harder99,
49	kreyscher00, zhang98, hunke97}, although there are sea ice models
50	diretized on a C-grid \citep[e.g.,][]{ip91, tremblay97,
51	lemieux09}. %
52	\ml{[there is also MI-IM, but I only found this as a reference:
53	\url{http://retro.met.no/english/r_and_d_activities/method/num_mod/MI-IM-Documentation.pdf}]}
54	From the perspective of coupling a sea ice-model to a C-grid ocean
55	model, the exchange of fluxes of heat and fresh-water pose no
56	difficulty for a B-grid sea-ice model \citep[e.g.,][]{timmermann02a}.
57	However, surface stress is defined at velocities points and thus needs
58	to be interpolated between a B-grid sea-ice model and a C-grid ocean
59	model. Smoothing implicitly associated with this interpolation may
60	mask grid scale noise and may contribute to stabilizing the solution.
61	On the other hand, by smoothing the stress signals are damped which
62	could lead to reduced variability of the system. By choosing a C-grid
63	for the sea-ice model, we circumvent this difficulty altogether and
64	render the stress coupling as consistent as the buoyancy coupling.
65
66	A further advantage of the C-grid formulation is apparent in narrow
67	straits. In the limit of only one grid cell between coasts there is no
68	flux allowed for a B-grid (with no-slip lateral boundary counditions),
69	and models have used topographies with artificially widened straits to
70	avoid this problem \citep{holloway07}. The C-grid formulation on the
71	other hand allows a flux of sea-ice through narrow passages if
72	free-slip along the boundaries is allowed. We demonstrate this effect
73	in the Candian Arctic Archipelago (CAA).
74
75	Talk about problems that make the sea-ice-ocean code very sensitive and
76	changes in the code that reduce these sensitivities.
77
78	This paper describes the MITgcm sea ice model; it presents example
79	Arctic and Antarctic results from a realistic, eddy-permitting, global
80	ocean and sea-ice configuration; it compares B-grid and C-grid dynamic
81	solvers and investigates further aspects of sea ice modeling in a
82	regional Arctic configuration; and it presents example results from
83	coupled ocean and sea-ice adjoint-model integrations.
84
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